The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, ...

Let F, N, A and N-2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FN-groups. We show that the property FC ...

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the lambda-statistical convergence of sequence ...

In the paper, we define Laguerre-based Hermite-Bernoulli polynomial with its generating function, and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series ...

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We ...

Motivated by Kurt's blending generating functions of q-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized ...

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several ...

In this paper, the class of q-Sheffer-Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of ...

In this paper, we introduce a generating function for a new generalization of Laguerre-based Apostol-Bernoulli polynomials, Apostol-Euler and Apostol-Genocchi polynomials. By making use of the generating function method ...